Finite Group Databasebeta

← #31806941

Subgroups — #31806941

Order 17792.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581527C211yesmaximal, characteristic
2#22580971C212yesmaximal
3C2×#17984761C211yesmaximal, characteristic, complemented
4#22580709C212yesmaximal, complemented
5#519×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2211yescharacteristic
7C2×#14555769C2212yes—
8#17984840C412yescomplemented
9#17984831C412yescomplemented
10#17984825—22no—
11#17984818—22no—
12#17984801C2211yescharacteristic
13#17984770—24no—
14#17984761—22no—
15C22×Q8×C139C2211yescharacteristic
16C4×Q8×C139—24no—
17#117×C139—22no—
18#117×C139C2212yes—
19#14555785—22no—
20#14555785—22no—
21C2×Dic278C2×C411yescharacteristic
22C2×D556C2×C411yescharacteristic
23C2×C22⋊D139—21no—
24C2×C4×D139—21no—
25#14555769—22no—
26#14555769—22no—
27C2×C139⋊C8—22no—
28C4⋊Dic139—21no—
29Dic139⋊C4—24no—
30C22⋊Dic139—21no—
31(C2×D139)⋊C4—24no—
32C4×Dic139C2×C412yes—
33C2×Q8×C139—22no—
34C2×Q8×C139—22no—
35C2×Q8×C139C2×C412yes—
36C2×Q8×C139D412yes—
37C22×C4×C139D412yes—
38C22×C4×C139C2311yescharacteristic
39C4⋊C4×C139—24no—
40C4⋊C4×C139—22no—
41C22⋊C4×C139—22no—
42C42×C139—24no—
43C42×C139D414yes—
44C22×D139—21no—
45Dic278—22no—
46D556—22no—
47C22⋊D139—41no—
48C22⋊D139—41no—
49C2×Dic139—22no—
50C2×Dic139—21no—
51C4×D139—42no—
52C139⋊C8—42no—
53C23×C139C2×D411yescharacteristic
54Q8×C139—24no—
55Q8×C139—24no—
56C2×C4×C139—22no—
57C2×C4×C139—22no—
58C2×C4×C139—24no—
59C2×C4×C139C22⋊C414yes—
60C2×C4×C139C22×C411yescharacteristic
61C2×C4×C139C2×D412yes—
62C2×C4×C139C2×D411yescharacteristic
63C2×C4×C139#4112yes—
64C22×C139—41no—
65C22×C139C2×C22⋊C411yescharacteristic
66C22×C139#12011yescharacteristic
67C22×C139#12311yescharacteristic
68C2×D139—42no—
69C2×D139—41no—
70C4×C139—24no—
71C4×C139—44no—
72C4×C139C4×D412yes—
73C4×C139#12112yes—
74Dic139—42no—
75Dic139—41no—
76C2×C139—21no—
77C2×C139—21no—
78C2×C139—21no—
79C2×C139#38611yescharacteristic
80D139—81no—
81C139#191211yescharacteristic, complemented, Sylow
82#1912—1391nomaximal, Sylow
83#536—1391no—
84#519D13911yescharacteristic, complemented
85#421—1392no—
86C2×#101—1391no—
87H(3,ℤ/4)—1392no—
88C2×#41—1391no—
89C22×Q8C2×D13911yescharacteristic
90C2×M16—1392no—
91C4⋊Q8—1392no—
92#124—1392no—
93#123—2782no—
94C22⋊Q8—2782no—
95C4×Q8—24no—
96#117—22no—
97#117—1391no—
98#117C2×D13912yes—
99#104—2784no—
100#101—2782no—
101#41—2782no—
102#41—2782no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1391no—
106C2×Q8C4×D13912yes—
107C2×Q8D55612yes—
108C2×D4—2781no—
109C2×D4—1391no—
110C22×C4—2781no—
111C22×C4C22⋊D13912yes—
112C22×C4C22×D13911yescharacteristic
113M16—2782no—
114M16—2782no—
115C2×C8—2782no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—2784no—
119C4⋊C4—2781no—
120C22⋊C4—22no—
121C22⋊C4—2781no—
122C22⋊C4—2784no—
123C42—24no—
124C42—1392no—
125C42C22⋊D13914yes—
126C23—2781no—
127C23C2×C22⋊D13911yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—2782no—
131D4—2782no—
132D4—5561no—
133D4—5561no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—2782no—
138C2×C4—2781no—
139C2×C4—5562no—
140C2×C4(C2×D139)⋊C414yes—
141C2×C4C2×C4×D13911yescharacteristic
142C2×C4C2×C22⋊D13912yes—
143C2×C4C2×D55611yescharacteristic
144C2×C4#1455578512yes—
145C8—5562no—
146C22—41no—
147C22—5562no—
148C22—5561no—
149C22C2×(C2×D139)⋊C411yescharacteristic
150C22#1798481111yescharacteristic
151C22#1798482511yescharacteristic
152C4—24no—
153C4—44no—
154C4—5562no—
155C4—5561no—
156C4C4×C22⋊D13912yes—
157C4#1798481612yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—11121no—
162C2#2258083211yescharacteristic
subgroupG/H
centerC2#22580832
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#519×C139C2
socleC2×C139#386
prime radicalC2×#14555785C22
cosocleC22×C4×C139C23
hypercenter#519D139
hypocenterC139#1912
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#17984761C2semidirect
4. #22580709C2semidirect
5. #519×C139C2semidirect
8. #17984840C4semidirect
9. #17984831C4semidirect
81. C139#1912semidirect
84. #519D139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225815272
#225809712
C2×#179847612
#225807092
#519×C1392
#1912139